An efficient algorithm for checking the robust stability of a polytope of polynomials |
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Authors: | Athanasios Sideris |
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Affiliation: | (1) Department of Electrical Engineering, 116-81, California Institute of Technology, 91125 Pasadena, California, U.S.A. |
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Abstract: | An efficient algorithm for checking the robust stability of a polytope of polynomials is proposed. This problem is equivalent
to a zero exclusion condition at each frequency. It is shown that such a condition has to be checked at only afinite number of frequencies.
We formulate this problem as aparametric linear program which can be solved by the Simplex procedure, with additional computations between steps consisting of polynomial evaluations
and calculation of positive polynomial roots. Our algorithm requires a finite number of steps (corresponding to frequency
checks) and in the important case when the polytope of parameters is a hypercube, this number is at most of orderO(m
3
n
2), wheren is the degree of the polynomials in the family andm is the number of parameters.
Supported by NASA under Contract No. NCC2-477 and by a Charles Powell Foundation Grant. |
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Keywords: | Robust stability Parametric uncertainty |
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